Äîêóìåíò âçÿò èç êýøà ïîèñêîâîé ìàøèíû. Àäðåñ îðèãèíàëüíîãî äîêóìåíòà : http://hbar.phys.msu.ru/gorm/ahist/antikythera5.pdf Äàòà èçìåíåíèÿ: Thu Nov 30 00:00:00 2006 Äàòà èíäåêñèðîâàíèÿ: Mon Oct 1 21:09:16 2012 Êîäèðîâêà:

doi: 10.1038/nature05357

SUPPLEMENTARY INFORMATION

CONTENTS Supplementary Notes 1 (Fragments) giving a key to fragment identification for Figure 1 of the main text and the dimensions of the fragments. Supplementary Notes 2 (Glyphs & Inscriptions)) giving details of the script of the characters, their dating and the Greek text and its provisional translation from (a) the Front Door inscriptions, (b) the Back Door inscriptions and (c) the Back Plate inscriptions near the Lower Back Dial. Supplementary Notes 3 (Gears) giving a table to compare gear nomenclature and the gear tooth count estimates with previous estimates and to tabulate measured radii. Some notes are given on the individual gears and on the tooth count estimation procedure, including the effects of uncertainty in determining the centres of the gears. The gear train ratios are explained on the basis of simple Babylonian period relations. The equivalence of the epicyclic gearing and pin-and-slot mechanism to Hipparchos' theory of the moon is proved.

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Supplementary Notes 1 (Fragments) Key to Figure 1 of the main text:

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Fragment

A B C D E F G 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36

Area of maximum section [cm2] 224.209 66.692 65.767 15.491 12.623 50.197 68.757 39.189 16.018 14.154 12.195 8.041 7.166 5.846 5.383 3.512 2.296 1.262 1.878 1.062 1.091 0.733 0.629 0.658 0.438 12.822 5.920 5.651 9.547 7.570 2.153 1.945 2.951 2.873 3.379 3.402 1.385 9.414 8.585 2.170 0.286 0.222 0.180

Weight [g] 369.1 99.4 63.8 15.0 22.1 86.2 31.7 62.5 15.3 23.5 9.6 6.2 10.9 7.0 3.2 1.7 1.2 0.7 0.6 02 0.2 0.1 0.3 0.2 0.1 5.2 2.2 2.0 2.7 5.8 0.5 0.6 1.1 1.5 1.1 1.0 0.3 15.8 14.9 1.1 >0.1 0.1 0.1

Thickness of discernible layers (mm)

7.6 (6 layers)

2 (1 layer) 3.2 (3 layers)

1.58 (1 layer) 1.24(1 layer), 1.0 (1 layer) 1.0 (1 layer) 1.6 (1 layer) 6.9 (6 layers) 1.0 (1 layer) 1.0 (1 layer) 2.6 (1 layer) 5.3 (5 layers) 1 mm (1layer) 2.8 (2 layers) 2.1 (1 layer) 1.5 (1 layer)

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37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75

2.027 1.575 1.376 1.026 1.228 0.724 1.079 0.954 1.660 0.592 0.911 0.395 0.489 0.322 1.108 0.781 0.849 0.651 0.881 0.497 0.346 0.565 0.285 0.604 0.456 0.357 0.334 0.237 0.266 0.208 0.528 0.208 0.187 0.238 0.270 0.270 0.485 0.201 0.146

0.7 0.5 0.4 0.3 0.5 0.2 0.3 0.4 0.6 0.2 0.3 0.1 0.1 0.1 0.2 0.3 0.3 0.2 0.2 0.2 0.1 0.2 0.1 0.1 0.1 0.1 0.1 >0.1 >0.1 0.1 0.2 0.1 >0.1 >0.1 0.1 0.1 0.1 0.1 0.1

1.6 (1 layer) 1.5 (1 layer) 1.7 (1 layer)

1.5 (1 layer)

1.5 1.9 1.2 2.1 1.7 1.0 1.0

(1 (1 (1 (1 (1 (1 (1

layer) layer), layer) layer) layer) layer), layer)

1 (1 layer)

For the dimensions in column 2 we have used digital scans of photographs, taken for us by Costas Xenikakis. The surface area in column 2 is the surface area of the largest section of each fragment (horizontal section, after positioning it down flat on a horizontal surface). Areas were estimated from prints of A4 images by squarecounting using transparent-millimeter-graph-paper. Image distortion was checked to be small from horizontal and vertical scales photographed with the fragments. The errors in area measurement are estimated as certainly no more than 0.01 cm2 The thickness of most of the metal sheets appears to be from 1 mm up to 2 mm, except for fragment 26, which is has a layer of 2.6 mm.

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Supplementary Notes 2 (Glyphs and Inscriptions) Glyphs

The 16 observed "Glyphs" from the Lower Back Dial. The lunar month number around the Saros dial is shown below each glyph. The data for the glyphs is transcribed directly from the PTMs in the rare cases when it is visible on the surface (e.g. Glyph 206), or from the CT when it is not (e.g. Glyph 218). Glyph 206 was noted by Price but not interpreted. Nearly all contain (lunar eclipse, from , Moon) or H (solar eclipse, from , Sun). We classify the glyphs into lunar, solar and lunar & solar, making reasonable inferences where there is only partial information. In the period 400-1 BC there are 121 possible start dates where the month sequence of glyphs exactly match not only the eclipses but also eclipse type. Where there is a lunar & solar glyph, both types occur in the same month. The anchor-like symbol is probably the "omega-rho" denoting "hour" (hora) ­ probably indicating the predicted hour of the eclipse after sunrise or after sunset. The hour is indicated by a Greek letter used as a numeral, including in its early form for the number 9. The same symbol also appears in the Parapegma inscription. The eta with mu above it (e.g. in the right hand column of Glyph 218) may be the standard abbreviation of "day" (hemera) ­ possibly indicating that the (predicted lunar) eclipse was diurnal. Inscriptions Mirror image script found on some fragments is probably due to the accretion of fine silt against the original inscriptions, which became infused with bronze corrosion products and set in a hard matrix against the original. The style of writing is almost identical on the different fragments, except for the text near the Lower Back Dial,
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whose variation could be due either to the smallness of the characters or to a different hand. Full details of variant readings and translations of all the inscriptions will be published in due course
Size (mm) Fragment A-2 A-2 B-1 B-1 C-1 C-1 C-2 E-1 D E-2 F G-1 19-1 20-1 21-1 22-1 24-1 25-1 Position Back door plate Lower back dial Back door plate Upper back scales Parapegma Front scales Parapegma Back door plate Gear (internal) Lower back dial Lower back dial Front door plate Back door plate Parapegma Front door plate? Parapegma Lower back dial ? Text Astronomic Misc. Astro/Mech Calendrical? Calendrical Calendrical Calendrical Mechanical Misc. Misc. Astronomic Astro/Mech Calendrical Astronomic Calendrical Glyph Type Mirror Direct Mirror Direct Direct Mirror Mirror Direct Direct Direct Direct Direct Mirror Direct Direct A 1.2 2.0 2.8 2.7 2.0 1.3 1.6 1.9 2.3 2.6 1.9 2.4 I 2.1 3.4 5.0 6.0 3.6 2.3 2.7 2.5 3.5 2.5 5.0 Characters in Price (1974) OK ? Total 97 24 121 46 17 63 157 41 198 95 12 107 23 0 23 13 0 13 153 27 180 117 10 127 6 0 6 45 10 55 21 0 21 Characters by this work OK ? Total 185 8 193 51 20 71 239 105 344 5 10 15 105 10 115 23 0 23 16 0 16 109 8 117 6 0 6 10 7 17 77 10 87 785 147 932 124 1 125 5 0 5 39 16 55 24 8 32 6 1 7

In addition to these, there are visible traces of inscriptions on fragments 23-2, 26-1, 28-1, 29-1, 37-1 to 44-1, 51-2, 53-2, 61-1 and 67-2. A classification of fragments with visible inscriptions could also be made based on the colour surface texture and colour, which, together with text size and type, will help in assembling texts from disparate minor fragments. The "?" indicates a doubtful transcription. Fragment D has the letters "ME" at three different places on a gear wheel. More isolated characters will become available as reconstruction from the CT scans of smaller fragments is completed Totals: Price 923, this work 2160. (A portion of 19-1 is counted twice in B-1, and some minor inscription is not included in the table above) Data from the PTM has proved to be invaluable in inspecting the surface of the fragments and the inscriptions. The CT, whose primary aim was to collect information about the internal structure of the Mechanism, has allowed the discovery of unknown characters within fragments A, B, C, D, E, F and G, and within some of the smaller fragments. The case of Fragment G is exemplary: Price (1974) notes that its inscription is "almost illegible', reading only 180 characters. The CT images, viewed at various angles, enable us to read 932 characters. The inscription on the fragment F (newly discovered and identified by M. Zafeiropoulou in 2005) has characters whose height is often less than 1.6 mm, totally invisible because they are covered by sea accretions. We propose two reconstitutions: the text from the back door plate, where part of the gap in Price (1974) is completed with text from Fragment E. Based on the internal structure of the fragment, showing portions of the scales, we are able to establish where the first line from fragment E joins with line 28 from fragment B1 and where the last line from fragment E joins with line 34 belonging to the fragment A2 (line 30 in Price). Similar results were produced with the text near the lower back dial, at the right side of the Mechanism. We are able to join characters from fragments A, E and F. We also believe that some characters in smaller fragments may join with the big and intriguing text from fragment G.

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The surviving part of the Front Door Plate probably comes from the middle of the original plate and we unfortunately lack the beginning and the end of phrases, and, because of this, possible planet names that would greatly aid interpretation. The mechanical terms of fragment E (trunnions, pointers and gears) are common in Heron's "Dioptra". The frequency of the (Parapegma) key letters in the Zodiac signs on the Front Dial suggest that the 24 letters of the greek alphabet might have been used twice here.

The figure shows an example of part of the inscription from the Back Door Plate on fragment 19, enhanced by the PTM technique. According to Haralambos Kritzas (Director Emeritus of the Epigraphic Museum, Athens) the style of the writing could date the inscriptions to the second half of the 2nd Century BC and the beginning of the 1st Century BC, with an uncertainty of about one generation (50 years). Dates around 150 BC to 100 BC are a plausible range. We give here a few examples of the epigraphic clues to the dating, but detailed analysis will be published elsewhere: pi has unequal legs - second half of 2nd century BC sigma has the two lines not horizontal but at an angle - second half of 2nd century BC, beginning of 1st century BC mu has the two lines not vertical but at an angle - second half of 2nd century BC. There is one M with vertical lines Y upsilon has the vertical line short - second half of 2nd century BC alpha - just post Alexander zeta is written like I with long horizontal lines - 2nd century BC omega and not like - 2nd century BC beta unequal upper circle, compared with the lower circle - old omicron very small - old theta has a short line in the middle, in one case a dot - 2nd century BC phi is arc like - old xi middle line short - old

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Greek Text of Front Door Inscription Mainly from fragment G. Red indicates dubious characters
1 2 3 4 5 6 7 8 9 10 [ ] [] [ ] 11 [ ] [ ] 12 [ ] [] 13 [] 14 [ ] [ ] [ ] 15 [ ] [ ] [ ] 16 [ ] [ ] [ ] 17 [ ] 18 [ ] 19 20 [ ] 21 22 [ ] 23 24 [ ] [ ] 25 / 26 [] 27 28 K [] 29 30 31 [] 32 33 34 35 [ ] 36 37 T H

Greek Text of Back Door Inscription Black and blue letters are believed to be good, red and orange are dubious. Black and red are from fragments A and B, blue and orange from fragment E. The second column in line numbering in Price (1974: reference 1 of main paper)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

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20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51

20 21 22 23 24 25 26 27 28 30 31 32 33 34 35 36 37 38 39 40 41 C L L 42 43 44 45 46 47

Greek Text of Back Plate inscription, near the Lower Back Dial Black and blue letters are believed to be good, red and orange are dubious. Black and red are from fragments A and F, blue and orange from the other side of fragment E.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

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16 17 18 / / 19 20 21 22 23 24 25 26 27 28 29 2 30 31 32 33 34

Table 1. Provisional Translation of the Front Door Inscriptions
1. --2. --3. --4. space (or distance) between 5. from the beginning 6. --7. --- restore (or which has been restored) 8. --9. towards the Sun <370> 10 .equal and brings the Sun upon to the equal

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11. brought upon the Sun the minor stationary point then occurs distance 12. brings towards the Sun up to --- and conjunction 13. on to the maximum following within other days 14. [stationa]ry point as the previous one 39 15. day, makes before one to the 16. interval brings upon to the 17. --18. the Sun 19. brings upon every (verb could be coincide) 20. brings upon [days] 21. days and remains until the eastern (eastern = adjective in the sense of dawn) 22. 34<0?> days 270 days --23. the stationary point which is at equal distance, is at a distance from the Sun 24. 265 of the Sun, extend the distance 25. 265 of the Sun, has extended four and one seventh 26. 8 days --- of the origin --- dawn 27. interval (or separation, length, distance; greek: diastasin) <2??> large days 28. twelfth part of the circle (greek: dodecatemorios) --- subtract the remaining (genre is feminine) 29. from the evening --- and the remaining 30. in time --- <370> days 31. brings on <139> the Sun the stationary point 32. days 31 is leading <37?> days 33. of the rising is the Sun 40 days

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34. day is becoming the 35. 205 days days from 36: --37: --Conventions used: --- : either unreadable, or non-translatable string < > : enclosing either dubious characters or one amongst many reading choices (e.g. either number or beginning of word) [ ] : enclosing restored sections ? : uncertain character

( ) : alternative translation, indication of greek word translated or (if in italics) comment from reader-translator.

Table 2. Provisional Translation of the Back Door Inscriptions
1. this 2. --3. and under the 4. --5. --6. --7. --8. --9. (of the) extremity 10. --11. ---

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12. --13. --14. [and is carrying] little [golden] sphere 15. the pointer that protrudes from it 16. carries, of which the next one 17. which is carried through (or the other carried by it) 18. of Venus 19. --20. on the [extremity of] the pointer stands a little golden sphere (golden or goldish) 21. the ray [towards the] Sun and above, the Sun is --22. --- when it moves through (through its orbit; greek: diaporevomenon) 23. --- and the moving through (same meaning as in line 22) 24. --- circle and the little sphere 25. stands --- the [sphere] of the world (world in greek:cosmos) 26. --- elements --27. --28. --29. the spiral divided in 235 sectors 30. and days to be excluded 2? (twenty to twenty-nine; "excluded" means "taken out of the calendar") 31. --- two trunnions (greek: stematia) around gear (greek: tympanon) 32. --- perforated trunnions (possibly pre-perforated) 33. through the perforations to be pulled (haul) 34. the same manner as

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35. --36. --37. --38. --39. --40. --41. from where it came out of 42. the first position 43. two pointers, whose ends carry 44. four, the one indicates 45. the 76 years, 19 years of the 46. 223 coming together 47. so that the whole will be divided 48. (of the) ecliptic 49. similar to those on the 50. carries 51. --Conventions used: see Table 1

No translation of the Back Plate Inscriptions, near the Lower Back Dial is attempted, as the text is rather incomplete. Work is in progress.

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Supplementary Notes 3 (Gears) The first publication that comprehensively estimated the tooth counts of the gears was Price's Gears from the Greeks (1974 - reference 1 in the Main Text). The original counts were done for Price by Charalambos and Emily Karakalos (based on conventional film x-radiography). These counts were then adapted by Price to suit his model. M.T. Wright has subsequently re-counted the teeth on digitised X-rays (with some limited use of tomography) undertaken by Bromley and Wright in 1990-1994. Our estimates are based on our CT data.
Gear Gear Price A B1 B2 B3 B4 C1 C2 D1 D2 E1 (E2i) E4 E3 (E2ii ) E5 F1 F2 G2 G1 H1 H2 I (K1) K2 L1 L2 M1 M2 Gear Wright A B6 B1 B2 B3 B4 B6 C1 C2 D1 D2 E6 E7 E4 E3 E8 E5 F1 F2 G2 G1 H1 H2 I K3 K2 L1 L2 M1 M2 N1 N2 O P1 P2 Q 1 2 Average outer radius to gear tips mm 13.6±0.2 64.9±1.1 15.5±0.2 8.6±0.2 10.3 11.3 5.6 31.6 9.4 7.8 52.6 50.2 13.4 13.9 14.0 8.3 14.2 4.9 14.0 3.9 13.4 13.5 14.0 9.1 13.1 24.5 4.4 ±0.3 ±0.4 ±0.3 ±0.2 ±0.3 ±0.2 ±0.3 ±0.3 ±0.2 ±0.2 ±0.2 ±0.3 ±0.3 ±0.1 ±0.1 ±0.2 ±0.3 ±0.3 ±0.2 ±0.2 ±0.4 ±0.5 ±0.3 Inner radius from bestfit circle ±0.5 mm Outer radius from best-fit circle ±0.5 mm Karakalos tooth count Price tooth count 45(48) 63.8 14.9 8.2 9.4 10.5 5.1 30.6 8.6 7.1 51.5 49.1 12.2 12.9 13.6 7.4 13.4 4.1 13.0 3.0 12.6 12.6 13.1 8.3 12.5 23.6 3.7 65.0 15.7 9.3 10.3 11.0 5.8 31.7 9.7 7.8 52.4 49.9 13.1 13.9 14.6 8.2 14.4 4.9 13.7 3.8 13.2 13.3 14.0 9.0 13.3 24.7 4.0 223-226 64-66 32 32 38 48 [24] 128 32? 32? 222 192 (32?) 50-52 54 30 54/55 20 60-62 16 60 (32) 48 or 51 36+ 52 96+ 14 225 64 32 32 38 48 24 127 32 32 222 192 Wright tooth count 48 223 64 32 24 38 48 24 127 32 32 223 191 51 53 54 30 55 20 60 15 60 49 49 38 53 96 15 53 15 60 60 12 24 63 65 Wright limits 44-52 216-231 Our best fit tooth count 48 20 223 64 32 38 47/48 24 127 32 32 220-225 187-191 52 50 53 30 54 20 60-64 15 60 49/50 50 38 53 96/97 15 Our limits Definite 223/224 64-66 Definite 38/39 47-49 Definite Definite Definite Definite 217-235 180-192 50-52 49/50 53/54 Definite 54-56 Definite 60-64 Definite 59-62 48-51 48-52 Definite Definite 96-99 Definite

a1 b0 b1 b2 b3 b4 c1 c2 d1 d2 e1 e2 e3 e4 e5 e6 f1 f2 g1 g2 h1 h2 i1 k1 k2 l1 l2 m1 m2 m3 n1 n2 o1 p1 p2 q1 r1

47-48

218-228 188-192 50-52 51-55 53-54 54-55 20 57-64 59-60 48-50 48-50 37-38 95-98

48 48 30 60 20 60 15 60 48 36 54 96 16

13.3±0.1

12.2

12.8

57-62

60*

57-61

N

5.3±0.2 16.4±0.2

15.9

16.9

63

64

20 63

Definite Definite

*Strong preference

(In the table: Price, Karakalos and Wright data taken from Wright, M.T., Bull.Sci.Instr.Soc. 85, 2-7, 2005 ­ reference 4 in the Main Text) Columns 3-5 give measured radii from CT data. Column 3 is the mean of the radii to the tooth tips from the assumed centres. Columns 4 and 5 gives the radii of "best fit" circles to the pits between the teeth (inner radius) and to the tooth tips (outer radius), with an estimated error of order or less than 0.5 mm. Gears in italics are hypothetical.

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Tooth Counting Method The angular data i of tooth tips from the centre is compared with a model a + n . The "goodness-of-fit" is the parameter =

[ - (a
n n

+ n

)]2

where n is

chosen as the model point closest to the data point. The shift parameter a is fixed to minimise by requiring that i = (a + i ) . We then investigate peaks in 1 /
i i

as a function of = 360 / T where T is the implied total number of teeth on the gear, i.e. we seek to minimise . If the errors in the angular data are Gaussian, this should give a "maximum likelihood" estimate of the true total tooth count. The counts are sensitive to the positioning of the assumed centre of the gear. This can be investigated by transformation from a measured set of data (see below), and we endeavour to find the "best" fit ­ i.e. strongest peak in 1 / - for reasonable variation of the centre position. In some cases a unique tooth count gives a very clear isolated peak, in other cases a range of peaks implies a range of possible total tooth counts, with adopted values implied (subjectively) from the relative peak heights. Gear Count Analysis: Moving the Centre Consider a measured tooth tip T at angle from a given centre O, with a measured distance r from the centre to the tooth tip. Now move the centre to O by a distance r in direction . The new angle of T from O is where:

T

r O O r

r'

In triangle